Adult film actress Stephanie Clifford, also known as Stormy Daniels, poses for pictures in Long Island, New York, on February 23, 2018. Eduardo Munoz / Reuters

Stormy Daniels, the adult film star who says she was paid to keep quiet about an affair with Donald Trump, is suing the president alleging that a non-disclosure agreement is invalid, bringing fresh turmoil to the White House as Texas voters offered the first sign of a Democratic surge.

The actress, whose real name is Stephanie Clifford, says the agreement, drafted before the 2016 election, is void because Mr Trump did not sign it.

It marks a fresh twist in a deeply embarrassing scandal that surfaced last month when Mr Trump’s personal lawyer, Michael Cohen, confirmed he had paid her $130,000 (Dh477,400).

Ms Clifford alleges that Mr Cohen tried to "intimidate her into silence", according to court documents.

The suit was filed in Los Angeles on Tuesday, the same day that voters in Texas went to the polls in the first primaries of the year and the White House announced that Gary Cohn was to resign as Mr Trump’s most senior economic adviser.

No reason was given but he was understood to have opposed the president’s plan to impose swingeing tariffs on imports of steel and aluminium as part of a populist, protectionist package.

The latest headlines add to a never-ending sense of crisis in Mr Trump’s administration, following the resignation of Hope Hicks as director of communications last week and Republican divisions over his tariffs.

Staff turnover is more than double that was seen in the Reagan administration and more than triple that of the Obama White House, according to a recent study by the Brookings Institution.

For his part, Mr Trump played down reports that more high-profile resignations would follow.

Plenty of people want to work at the White House, he said during a joint news conference with Sweden's prime minister.

“They all want a piece of that Oval Office,” he said. “They want a piece of the West Wing. And not only in terms of it looks great on their resume, it's just a great place to work.”

Meanwhile, the Stormy Daniels controversy shows no signs of dissipating. Her attorney published her legal complaint by sharing a link on Twitter.

In it, she claims to have had an affair with Mr Trump several years before he ran for office, in 2006.

Mr Trump married his current wife, Melania, in 2005.

Ms Clifford says she was later approached by his lawyers during the campaign – at a time when multiple women were coming forward with their own stories about alleged affairs or encounters with the New York property mogul.

A hush agreement was drawn up using aliases of Peggy Peterson and David Dennison. Her suit claims it was never signed by Mr Trump and that his lawyers have tried to prevent her speaking publicly.

“To be clear, the attempts to intimidate Ms Clifford into silence and ‘shut her up’ in order to ‘protect Mr Trump’ continue unabated,” it says.

On Wednesday, her lawyer, Michael Avenatti, appeared on US morning news shows to say that Mr Trump knew about the payment and that his client merely wanted to “set the record straight”.

Although the White House declined to comment on the new lawsuit, Mr Cohen has previously denied there was ever an affair.

Opponents of Mr Trump believe the non-stop controversies – a wide-ranging investigation into Russian election meddling, the president’s volatile style, and a looming trade war – will translate into a surge of anti-Trump votes at the ballot box later this year. Democrats are hoping they can regain control of the House of Representatives in November’s midterm elections.

They had their first glimpse of how that might unfold in Texas on Tuesday. Democrats turned out in numbers not seen for more than 15 years during the first primaries of the voting season.

Women performed particularly well – winning or proceeding to the next round in half the contests in which they ran – while Democratic turnout surged past one million voters.

“It’s Trump. It’s Trump,” said Veronica Escobar, who won her Democratic primary and is on course to become one of the first Hispanic women to represent Texas in Congress.

Mark Jones, a political science professor at Rice University in Houston, said highly motivated Democrats would have a strong showing in November.

“The enthusiasm advantage that Democrats have in 2018 compared to 2014 should help them pick off a few toss-up US Houses seats held by Republicans,” he said.

But at the same time, the votes demonstrated the president’s polarising effect and the challenges facing Mr Trump’s opponents. Republican turnout also increased in the staunch red state to more than 1.5 million.

Ted Cruz, the former presidential candidate and Texas senator who won his own primary, used the Democratic numbers to motivate Republicans.

"The extreme left right now is energised. They are angry. They hate the President,” he told CNN. “That being said, in Texas last night, we had a strong turnout for conservatives."